That's not really a lot of miles for that car - an accord that's been reasonably maintained should go 300k miles without a major system failure - engine / transmission. A wise man once told me that my car wasn't worth what he was willing to give me, but was actually worth what it would cost me to replace it. If its mechanically sound and does what you need it to do, just pay the $700 for a new converter, it should be fine. Now, if the normal maintenance hasn't been done regularly, you may be in the danger zone with a couple really big breakdowns and might want to bail on it.

I have 238k on mine and everything works. Go to Autozone ask them to pull the codes for you, they do it for free. Then look on Youtube for Eric the Car Guy, look for your problem on his site. There is usualy a video to fix it.

If it is the converter,reset the computer, go to Homedepot and buy 3 gallons of Lacquer thinner, pour it in the gas tank. Run a full tank of gas through it, if the light still comes on, take off the converter and let it sit in a solution of Dawn then run lacquer thinner through it again. It should work. If not look up a good after market CAT, and put a spark-arrestor on the sensor, problem solved. All of this can be found on the "internets". Eric's site will help you with almost any repair and he is usually working on a Honda in the video.